Creation of Tuning Rules for PID Controllers that Outperform the Ziegler-Nichols and Åström-Hägglund Tuning Rules

 

(A Human-Competitive Result Produced by Genetic Programming)

 

The Result

Genetic programming evolved tuning rules for PID controllers that outperform the Ziegler-Nichols and Åström-Hägglund tuning rules as described in 12 of Genetic Programming IV: Routine Human-Competitive Machine Intelligence (Koza, Keane, Streeter, Mydlowec, Yu, and Lanza 2003).

BBB3600

The topology (above) was not evolved, but was the standard PID topology.

Genetic programming evolved equations for Kp-final, Ki-final, Kd-final, and bfinal:

 

Kp-final =

Ki-final =

Kd-final =

bfinal =

Basis for Claim of Human-Competitiveness

The PID controller was patented in 1939 by Albert Callender and Allan Stevenson of Imperial Chemical Limited of Northwich, England (Callender and Stevenson 1939). The PID controller was an enormous improvement over previous manual and automatic methods for control.

In 1942, Ziegler and Nichols published a paper entitled “Optimum Settings for Automatic Controllers” in which they developed a set of mathematical rules for automatically selecting the parameter values associated with the proportional, integrative, and derivative blocks of a PID controller (Ziegler and Nichols 1942). The Ziegler-Nichols rules have been in widespread use for tuning PID controllers since World War II.

The quality of PID tuning rules is of considerable practical importance because a small percentage improvement in the operation of a plant can translate into large economic savings or other (e.g., environmental) benefits.

Åström and Hägglund improved on the 1942 Ziegler and Nichols in their important 1995 book PID Controllers: Theory, Design, and Tuning. In that book for four families of plants “that are representative for the dynamics of typical industrial processes.”

Genetic programming, in turn, has created new tuning rules for PID controllers (called the Keane-Koza-Streeter (KKS) rules) that are an improvement over the PID tuning rules developed by Åström and Hägglund in their 1995 book..

The genetically evolved PID tuning rules are an improvement over the 1995 Åström-Hägglund tuning rules.

Referring to the eight criteria in table 1.2 of Genetic Programming IV: Routine Human-Competitive Machine Intelligence (Koza, Keane, Streeter, Mydlowec, Yu, and Lanza 2003) for establishing that an automatically created result is competitive with a human-produced result, the creation by genetic programming of improved tuning rules for PID controllers satisfies the following five of the eight criteria:

(B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal.

(D) The result is publishable in its own right as a new scientific result¾independent of the fact that the result was mechanically created.

(E) The result is equal to or better than the most recent human-created solution to a long-standing problem for which there has been a succession of increasingly better human-created solutions.

(F) The result is equal to or better than a result that was considered an achievement in its field at the time it was first discovered.

(G) The result solves a problem of indisputable difficulty in its field.

A patent application (Keane, Koza, and Streeter 2002a) was filed on July 12, 2002, for the genetically evolved PID tuning rules. The applicants believe that the genetically evolved PID tuning rules are patentable because they satisfy the statutory requirements of being “new,” “useful,” “improved,” and “unobvious” to someone “having ordinary skill in the art.”

U.S. law suggests that inventions created by automated means are patentable by saying:

“Patentability shall not be negatived by the manner in which the invention was made.” (35 United States Code 103a)

If (as expected) a patent is granted, it will (we believe) be the first patent granted for an invention created by genetic programming.

We believe that the creation by genetic programming of improved tuning rules for PID controllers satisfies the following additional criterion from table 1.2 of Genetic Programming IV: Routine Human-Competitive Machine Intelligence:

(A) The result was patented as an invention in the past, is an improvement over a patented invention, or would qualify today as a patentable new invention.

References

Åström, Karl J. and Hägglund, Tore. 1995. PID Controllers: Theory, Design, and Tuning. Second Edition. Research Triangle Park, NC: Instrument Society of America.

Callender, Albert and Stevenson, Allan Brown. 1939. Automatic Control of Variable Physical Characteristics. U.S. patent 2,175,985. Filed February 17, 1936 in the United States. Filed February 13, 1935 in Great Britain. Issued October 10, 1939 in the United States.

Keane, Martin A., Koza, John R., and Streeter, Matthew J. 2002a. Improved General-Purpose Controllers. U.S. patent application filed July 12, 2002.

Koza, John R., Keane, Martin A., Streeter, Matthew J., Mydlowec, William, Yu, Jessen, and Lanza, Guido. 2003. Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Kluwer Academic Publishers.

Ziegler, J. G. and Nichols, N. B. 1942. Optimum settings for automatic controllers. Transactions of ASME. (64)759–768.

· The home page of Genetic Programming Inc. at www.genetic-programming.com.

· For information about the field of genetic programming and the field of genetic and evolutionary computation, visit www.genetic-programming.org

· The home page of John R. Koza at Genetic Programming Inc. (including online versions of most published papers) and the home page of John R. Koza at Stanford University

· For information about John Koza’s course on genetic algorithms and genetic programming at Stanford University

· Information about the 1992 book Genetic Programming: On the Programming of Computers by Means of Natural Selection, the 1994 book Genetic Programming II: Automatic Discovery of Reusable Programs, the 1999 book Genetic Programming III: Darwinian Invention and Problem Solving, and the 2003 book Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Click here to read chapter 1 of Genetic Programming IV book in PDF format.

· 3,440 published papers on genetic programming (as of November 28, 2003) in a searchable bibliography (with many on-line versions of papers) by over 880 authors maintained by William Langdon’s and Steven M. Gustafson.

· For information on the Genetic Programming and Evolvable Machines journal published by Kluwer Academic Publishers

· For information on the Genetic Programming book series from Kluwer Academic Publishers, see the Call For Book Proposals

· For information about the annual Genetic and Evolutionary Computation (GECCO) conference (which includes the annual GP conference) to be held on June 26–30, 2004 (Saturday – Wednesday) in Seattle and its sponsoring organization, the International Society for Genetic and Evolutionary Computation (ISGEC). For information about the annual Euro-Genetic-Programming Conference to be held on April 5-7, 2004 (Monday – Wednesday) at the University of Coimbra in Coimbra Portugal. For information about the 2003 and 2004 Genetic Programming Theory and Practice (GPTP) workshops held at the University of Michigan in Ann Arbor. For information about Asia-Pacific Workshop on Genetic Programming (ASPGP03) held in Canberra, Australia on December 8, 2003. For information about the annual NASA/DoD Conference on Evolvable Hardware Conference (EH) to be held on June 24-26 (Thursday-Saturday), 2004 in Seattle.

Last updated on December 27, 2003